Verify that the equation is an identity. \[ \cos ^{2} \theta\left(\tan ^{2} \theta+1\right)=1 \]

Realiza lo que se indica. Halla \( \alpha \) y \( \beta \) para que las relaciones sean válidus \( \tan \left(3 \alpha+15^{\circ}\right)=\cot \left(\beta+6^{\circ}\right) \) y \( \sec \left(\alpha+54^{\circ}\right)=\cos \left(2 \beta-12^{\circ}\right) \) \( \tan (3 \alpha+15)=\cot (\beta+6)(\sec (\alpha+54)=\cos (2 \beta-12) \)

Calcula las medidas de los tres ángulos \( \mathrm{A}, \mathrm{B} \) y C, si: \[ \begin{array}{l}\operatorname{sen}(\mathrm{A}-\mathrm{B})=\cos 70^{\circ} \\ \sec (\mathrm{C}-\mathrm{B})=\csc 50^{\circ} \\ \tan (\mathrm{A}+\mathrm{C}) \cdot \cot 80^{\circ}=1\end{array} \]

Solve the equation \( 5 \sin 2 x+2=0 \) for \( 0^{\circ} \leq x \leq 360^{\circ} \) Correct your answer to 1 decimal place.

(a) Solve the equation \( 5 \sin 2 x+2=0 \) for \( 0^{\circ} \leq x \leq 360^{\circ} \) Correct your answer to 1 decimal place.

Realiza lo que se indica. (12) Halla \( \alpha \beta \) yara que las relaciones sean válidas \( \tan \left(3 \alpha+15^{\circ}\right)=\cot \left(\beta+6^{\circ}\right) \) y \( \sec \left(\alpha+54^{\circ}\right)=\cos \left(2 \beta-12^{\circ}\right) \)